A set of agents with possibly different waiting costs have to receive the same service one after the other. Efficiency requires to maximize total welfare. Fairness requires to treat equal agents equally. One must form a queue, set up monetary transfers to compensate agents having to wait, and not a priori arbitrarily exclude agents from positions. As one may not know agents' waiting costs, they may have no incentive to reveal them. We identify the only rule satisfying Pareto-efficiency, equal treatment of equals in welfare or symmetry, and strategy-proofness. It satisfies stronger axioms, as no-envy and anonymity. Further, its desirability extends to related problems. To obtain these results, we prove that a rule, single-valued or not, satisfies queue-efficiency and strategy-proofness if and only if it always selects efficient queues and sets transfers à la Groves [Groves, T., 1973. Incentives in teams. Econometrica 41, 617-631]. This holds in other problems, provided the domain of quasilinear preferences is rich enough.
We consider two-sided many-to-many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling). We study when truncation / dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation / dropping strategies. We prove that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 1). We show that this result cannot be extended neither to group manipulations (even when all quotas equal 1-Example 1), nor to individual manipulations when the agent's quota is larger than 1 (even when all other agents' quotas equal 1-Example 2). Finally, we prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 2), i.e., independently of the quotas.
When allocating a resource, geographical and infrastructural constraints have to be taken into account. We study the problem of distributing a resource through a network from sources endowed with the resource to citizens with claims. A link between a source and a citizen depicts the possibility of a transfer from the source to the citizen. Given the endowments at each source, the claims of citizens, and the network, the question is how to allocate the available resources among the citizens. We consider a simple allocation problem that is free of network constraints, where the total amount can be freely distributed. The simple allocation problem is a claims problem where the total amount of claims is greater than what is available. We focus on resource monotonic and anonymous bilateral principles satisfying a regularity condition and extend these principles to allocation rules on networks. We require the extension to preserve the essence of the bilateral principle for each pair of citizens in the network. We call this condition pairwise robustness with respect to the bilateral principle. We provide an algorithm and show that each bilateral principle has a unique extension which is pairwise robust (Theorem 1). Next, we consider a Rawlsian criteria of distributive justice and show that there is a unique "Rawls fair" rule that equals the extension given by the algorithm (Theorem 2). Pairwise robustness and Rawlsian fairness are two sides of the same coin, the former being a pairwise and the latter a global requirement on the allocation given by a rule. We also show as a corollary that any parametric principle can be extended to an allocation rule (Corollary 1). Finally, we give applications of the algorithm for the egalitarian, the proportional, and the contested garment bilateral principles (Example 1).
We consider two-sided many-to-many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling).We study when truncation/dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation/dropping strategies. We prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 1), i.e., independently of the quotas. Then, we show that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 2). Finally, we show that this result cannot be extended neither to individual manipulations when the agent's quota is larger than 1 (even when all other agents' quotas equal 1 -Example 1), nor to group manipulations (even when all quotas equal 1 -Example 2).
We study many-to-one matching markets where hospitals have responsive preferences over students. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling. Roth and Sotomayor (1990) showed that equilibrium outcomes can be unstable. We prove that any stable matching is obtained in some equilibrium. We also show that the exhaustive class of dropping strategies does not necessarily generate the full set of equilibrium outcomes. Finally, we find that the 'rural hospital theorem' cannot be extended to the set of equilibrium outcomes and that welfare levels are in general unrelated to the set of stable matchings. Two important consequences are that, contrary to one-to-one matching markets, (a) filled positions depend on the equilibrium that is reached and (b) welfare levels are not bounded by the optimal stable matchings (with respect to the true preferences).
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